Reduced Model Unifying Frequency Combs in Ring and Fabry-Perot Quantum Cascade Lasers

We present a new theoretical model to study the spontaneous formation of frequency combs in quantum cascade lasers (QCLs). This model can reproduce comb emission in both ring and Fabry-Perot (FP) cavities. It consists of a single complex Ginzburg-Landau equation modified by a nonlocal integral term that accounts for the coupling between forward and backward fields in the FP configuration. The ring case is retrieved by setting this integral term to zero. Numerical simulations based on this model allow for reproducing numerous experimental features, such as the coexistence of amplitude and frequency modulations, linear chirp, and self-starting harmonic combs.